Consider the signal x[n] and the impulse response h[n] defined below: x[n] = u[n] − u[n...
Consider the signal x[n] and the impulse response h[n] defined below:
x[n] = u[n] − u[n − 49] h[n] = u[n] − u[n − 3].
Sketch y[n] = x[n] ∗ h[n] (the convolution of x[n] and h[n]). You must justify your answer by showing some intermediate calculations and/or sketches.
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Consider the signal x[n] and the impulse response h[n] defined
below:
x[n] = u[n] − u[n...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n]...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
(1) For the impulse response (h(t)) and input signal (x(t)) of an LTI system shown below,...
(1) For the impulse response (h(t)) and input signal (x(t)) of an LTI system shown below, find and plot the output response (y(t)) by integrating the convolution analytically h(t) x(t) t (s)
Question 2: (25 Marks) The Impulse response h(n) of a filter is non zero over the...
Question 2: (25 Marks) The Impulse response h(n) of a filter is non zero over the index range of n be [5,8]. The input signal x(n) to this filter is non zero over the index range of n be [7,12]. Consider the direct and LTI forms of convolution y(n)-Σh(m) x(-m)- Σχm)h (n -m) m a. Determine the overall index range n for the output y(n). For each n, determine the corresponding summation range over m, for both the direct and...
Question 5: (25marks) The Impulse response h(n) of a filter is non zero over the index range of n be [3,6]. The inp...
Question 5: (25marks) The Impulse response h(n) of a filter is non zero over the index range of n be [3,6]. The input signal x(n) to this filter is non zero over the index range of n be [10,20]. Consider the direct and LTI forms of convolution yin)-Σh(m) x (n-m)- Σχm)h (n -m) Determine the overall index range n for the output y(n). For each n, determine the corresponding summation range over m, for both the direct and LTI forms....
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2...
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2 zero . Determine the outputs when the input x(n) is (a) u(n ) ; (b) u(n−4 ) 2. Let the rectangle pulse x ( n )=u ( n ) −u (n −10 ) be an input to an LTI system with impulse response h (n )=(0.9 )n u (n ) . Determine the output y ( n ) . (Hint: You need to consider muliple...
I. Assume that the system impulse response h(t) is defined by h(y-exp-2) u(o (a) Calculate the...
I. Assume that the system impulse response h(t) is defined by h(y-exp-2) u(o (a) Calculate the Hin using the definition of Fourier Integral (Solve the integral) (b) Based on the results of part (a) you calculated, what do you think this system is? IGive reasoning for your answer!] (2) (e) For the signal x(-4Cos od +4 Sin'od, find All Complex (exponential) Fourier Series Coefficients Ca [Use formula sheet for Cos and Sine for exponential
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convol...
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
Consider the DT LTI system defined by the mpulse response h[n] = ?[n] The input to this system is the signal rn: ?[n-1) (a) Sketch h[n] and r[n] (b) Determine the output of the systern, ylnj, using convolution. Sketch y[n] (c) Determine the DTFTs H(e) and X(e. Make fully-labeled sketches of the magni- tudes of these DTFTs (d) Recall that the discrete Fourier transform (DFT) is simply defined as samples of the discrete-time Fourier transform (DTFT). Compute the 4-point (N-4)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
Consider that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1)
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
(1) For the impulse response (h(t)) and input signal (x(t)) of an LTI system shown below, find and plot the output response (y(t)) by integrating the convolution analytically h(t) x(t) t (s)
Question 2: (25 Marks) The Impulse response h(n) of a filter is non zero over the index range of n be [5,8]. The input signal x(n) to this filter is non zero over the index range of n be [7,12]. Consider the direct and LTI forms of convolution y(n)-Σh(m) x(-m)- Σχm)h (n -m) m a. Determine the overall index range n for the output y(n). For each n, determine the corresponding summation range over m, for both the direct and...
Question 5: (25marks) The Impulse response h(n) of a filter is non zero over the index range of n be [3,6]. The input signal x(n) to this filter is non zero over the index range of n be [10,20]. Consider the direct and LTI forms of convolution yin)-Σh(m) x (n-m)- Σχm)h (n -m) Determine the overall index range n for the output y(n). For each n, determine the corresponding summation range over m, for both the direct and LTI forms....
I. Assume that the system impulse response h(t) is defined by h(y-exp-2) u(o (a) Calculate the Hin using the definition of Fourier Integral (Solve the integral) (b) Based on the results of part (a) you calculated, what do you think this system is? IGive reasoning for your answer!] (2) (e) For the signal x(-4Cos od +4 Sin'od, find All Complex (exponential) Fourier Series Coefficients Ca [Use formula sheet for Cos and Sine for exponential
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum.
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
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